vinayparamanand wrote:

Four friends Laura, Nancy, James and Simon buy some pencils, pens and erasers from a shop. Laura buys 5 pencils, 6 pens, and 1 eraser for $17.50. Nancy buts 3 pens, 3 pencils, and 2 erasers for $ 10. James buys 5 pens, 2 pencils, and 5 erasers for $14.50. How much will Simon have to pay if he buys 3 pens, 2 pencils, and 5 erasers?

Note: How often in the GMAT do such questions appear?

Can i have a generic way to solve such questions?

A: $9.5

Let the cost of a pencil be $x

Let the cost of a pen be $y

Let the cost of a erasers be $z

Now,

for Laura 5x+6y+z = 17.50 ----a

for Nancy 3x+3y+2z=10 ----b

for James 2x+5y+5z=14.50 ---c

We have to find value for Simon i.e 3x+2y+5z=??

Now,

2b - a => x + 3z = 2.5 ----d

5b - 3c => 9x - 5z = 6.5 ------e

Solving, d and e

9d - e => 9x + 27z - (9x-5z ) = 22.5 - 6.5

32z = 16

z = 1/2

putting z in d, we get x = 1

putting z and x in a we get y= 2

3x + 2y +5z = 3 + 4 + 2.5 => 9.5$

Thanks,

Jai

KUDOS if it HELPED..!!!

_________________

MODULUS Concept ---> http://gmatclub.com/forum/inequalities-158054.html#p1257636

HEXAGON Theory ---> http://gmatclub.com/forum/hexagon-theory-tips-to-solve-any-heaxgon-question-158189.html#p1258308